I agree, I do not think I would say that “we have evidence that there is not a strong relation”. But I do feel comfortable saying that we do not have evidence that there is any relation at all.
The 95% confidence intervals are extremely wide, given our small sample sizes:
Spring 2019: −0.75 to 0.5 (95th) and −0.55 to 0.16 (75th)
Fall 2019: −0.37 to 0.69 and −0.19 to 0.43
Spring 2020: −0.67 to 0.66 and −0.37 to 0.37
Summer 2020: −0.60 to 0.51 and −0.38 to 0.26
The upper ends are very high, and there is certainly a possibility that our interview scoring process is actually good. But, of the observed effects, two are negative, and two are positive. The highest positive observed correlation is only 0.10.
To somebody who has never been to San Francisco in the summer, it seems reasonable to expect it to rain. It’s cloudy, it’s dark, and it’s humid. You might even bring an umbrella! But, after four days, you’ve noticed that it hasn’t rained on any of them, despite continuing to be gloomy. You also notice that almost nobody else is carrying an umbrella; many of those who are are only doing so because you told them you were! In this situation, it seems unlikely that you would need to see historical weather charts to conclude that the cloudy weather probably doesn’t imply what you thought it did.
This is analogous to our situation. We thought our interview scores would be helpful. But it’s been several years, and we haven’t seen any evidence that they have been. It’s costly to use this process, and we would like to see some benefit if we are going to use it. We have not seen that benefit in any of our four cohorts. So, it makes sense to leave the umbrella at home, for now.
Thanks for sharing the confidence intervals. I guess it might be reasonable to conclude from your experience that the interview scores have not been informative enough to justify their cost.
What I am saying is that it doesn’t seem (to me) that the data and evidence presented allows you to say that. (But maybe other analysis or inference from your experience might in fact drive that conclusion, the ‘other people in San Francisco’ in your example.)
But if I glance at just the evidence/confidence intervals it suggests to me that there may be a substantial probability that in fact there is a strongly positive relationship and the results are a fluke.
On the other hand I might be wrong. I hope to get a chance to follow up on this:
We could simulate a case where the measure has ‘the minimum correlation to the outcome to make it worth using for selecting on’, and see how likely it would be, in such a case, to observe the correlations as low as you observed
Or we could start with a minimally informative ‘prior’ over our beliefs about the measure, and do a Bayesian updating exercise in light of your observations; we could then consider the posterior probability distribution and consider whether it might justify discontinuing the use of these scores
I agree, I do not think I would say that “we have evidence that there is not a strong relation”. But I do feel comfortable saying that we do not have evidence that there is any relation at all.
The 95% confidence intervals are extremely wide, given our small sample sizes:
Spring 2019: −0.75 to 0.5 (95th) and −0.55 to 0.16 (75th)
Fall 2019: −0.37 to 0.69 and −0.19 to 0.43
Spring 2020: −0.67 to 0.66 and −0.37 to 0.37
Summer 2020: −0.60 to 0.51 and −0.38 to 0.26
The upper ends are very high, and there is certainly a possibility that our interview scoring process is actually good. But, of the observed effects, two are negative, and two are positive. The highest positive observed correlation is only 0.10.
To somebody who has never been to San Francisco in the summer, it seems reasonable to expect it to rain. It’s cloudy, it’s dark, and it’s humid. You might even bring an umbrella! But, after four days, you’ve noticed that it hasn’t rained on any of them, despite continuing to be gloomy. You also notice that almost nobody else is carrying an umbrella; many of those who are are only doing so because you told them you were! In this situation, it seems unlikely that you would need to see historical weather charts to conclude that the cloudy weather probably doesn’t imply what you thought it did.
This is analogous to our situation. We thought our interview scores would be helpful. But it’s been several years, and we haven’t seen any evidence that they have been. It’s costly to use this process, and we would like to see some benefit if we are going to use it. We have not seen that benefit in any of our four cohorts. So, it makes sense to leave the umbrella at home, for now.
Thanks for sharing the confidence intervals. I guess it might be reasonable to conclude from your experience that the interview scores have not been informative enough to justify their cost.
What I am saying is that it doesn’t seem (to me) that the data and evidence presented allows you to say that. (But maybe other analysis or inference from your experience might in fact drive that conclusion, the ‘other people in San Francisco’ in your example.)
But if I glance at just the evidence/confidence intervals it suggests to me that there may be a substantial probability that in fact there is a strongly positive relationship and the results are a fluke.
On the other hand I might be wrong. I hope to get a chance to follow up on this:
We could simulate a case where the measure has ‘the minimum correlation to the outcome to make it worth using for selecting on’, and see how likely it would be, in such a case, to observe the correlations as low as you observed
Or we could start with a minimally informative ‘prior’ over our beliefs about the measure, and do a Bayesian updating exercise in light of your observations; we could then consider the posterior probability distribution and consider whether it might justify discontinuing the use of these scores